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### Section 2.1 : Solutions and Solution Sets

For each of the following determine if the given number is a solution to the given equation or inequality.

1. Is $$x = 6$$ a solution to $$2x - 5 = 3\left( {1 - x} \right) + 22$$? Solution
2. Is $$t = 7$$ a solution to $${t^2} + 3t - 10 = 4 + 8t$$? Solution
3. Is $$t = - 3$$ a solution to $${t^2} + 3t - 10 = 4 + 8t$$? Solution
4. Is $$w = - 2$$ a solution to $$\displaystyle \frac{{{w^2} + 8w + 12}}{{w + 2}} = 0$$? Solution
5. Is $$z = 4$$ a solution to $$6z - {z^2} \ge {z^2} + 3$$? Solution
6. Is $$y = 0$$ a solution to $$2\left( {y + 7} \right) - 1 < 4\left( {y + 1} \right) + 3\left( {4y + 10} \right)$$? Solution
7. Is $$x = 1$$ a solution to $${\left( {x + 1} \right)^2} > 3x + 1$$? Solution